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Math Help - Negative binomial question with exact number

  1. #1
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    Negative binomial question with exact number

    This is a practice problem from Ross (A First Course in Probability)

    An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently agrees to be interviewed with probability 2/3, what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of (a) 5 people and (b) 8 people? For part (b), what is the probability that the interviewer will speak to exactly (c) 6 people and (d) 7 people?

    (a) and (b) were super easy... they were just a negative binomial dist with p= 2/3 and X=5 one for n=5 and one for n=8

    now for calculating the exact number, I am a bit confused. any hints?

    I'm usually a genius in this class but this problem has me stumped!

    I've tried everything
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  2. #2
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    Quote Originally Posted by douber View Post
    This is a practice problem from Ross (A First Course in Probability)

    An interviewer is given a list of people she can interview. If the interviewer needs to interview 5 people, and if each person (independently agrees to be interviewed with probability 2/3, what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of (a) 5 people and (b) 8 people? For part (b), what is the probability that the interviewer will speak to exactly (c) 6 people and (d) 7 people?

    (a) and (b) were super easy... they were just a negative binomial dist with p= 2/3 and X=5 one for n=5 and one for n=8

    now for calculating the exact number, I am a bit confused. any hints?

    I'm usually a genius in this class but this problem has me stumped!

    I've tried everything
    Let S represent - A person agrees for interview

    (c) Find prob of 5 S and 1 F. Arrangement can be of the form
    _ _ _ _ _ S

    (d) Find prob of 5 S and 2 F. Arrangement can be of the form
    _ _ _ _ _ _ S
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  3. #3
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    Quote Originally Posted by aman_cc View Post
    Let S represent - A person agrees for interview

    (c) Find prob of 5 S and 1 F. Arrangement can be of the form
    _ _ _ _ _ S

    (d) Find prob of 5 S and 2 F. Arrangement can be of the form
    _ _ _ _ _ _ S
    Wow thanks friend. Got it now...

    160/729

    makes sense now too!
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